The hydraulic flow of either a single layer or multiple layers of fluid over a topographic feature is frequently employed in many areas of civil engineering, meteorology, and oceanography. It is usually tacitly assumed that such flows remain attached as they flow over the topography. This paper determines the conditions under which flow separation occurs. Hydraulic equations for the horizontal velocity, and the criterion that separation occurs when the flow is locally decelerating are used to determine that for a single-layer separation occurs whenever the flow is everywhere subcritical. The results of experiments (in an open channel flume) are in agreement with this theoretical criterion. The analysis is extended to determine the condition under which a two-layer hydraulic flow separates.